Main Research

By Jack Wilburn

Libraries

library(readr)
library(mosaic)
library(gridExtra)
library(caret)
library(reshape)
library(car)
library(broom)
library(e1071)
library(leaps)
library(psych)

Importing and Cleaning Data

# execs import and cleaning
execs = read_csv("SeniorExecs.csv")
execs = execs[,c(1,2,4:37,44:54)]
execs$dimIPart1 = execs$DIMI1
execs$dimEPart1 = execs$DIME1
execs$dimSPart1 = execs$DIMS1
execs$intIPart1 = execs$INTI1
execs$intEPart1 = execs$INTE1
execs$intSPart1 = execs$INTS1
execs$difPart1 = execs$DIF1
execs$intPart1 = execs$INT1
execs$dimPart1 = execs$DIM1
execs$diPart1 = execs$DI1
execs$disPart1 = execs$DIS1
execs$VQ1 = execs$VQ1
execs$VQ2 = execs$VQ2
execs$dimPercPart1 = execs$DIMper1
execs$intPercPart1 = execs$INTper1
execs$aiPercPart1 = execs$AIper1
execs$dimIPart2 = execs$DIMI2
execs$dimEPart2 = execs$DIME2
execs$dimSPart2 = execs$DIMS2
execs$intIPart2 = execs$INTI2
execs$intEPart2 = execs$INTE2
execs$intSPart2 = execs$INTS2
execs$difPart2 = execs$DIF2
execs$intPart2 = execs$INT2
execs$dimPart2 = execs$DIM2
execs$diPart2 = execs$DI2
execs$disPart2 = execs$DIS2
execs$SQ1 = execs$SQ1
execs$SQ2 = execs$SQ2
execs$dimPercPart2 = execs$DIMper2
execs$intPercPart2 = execs$INTper2
execs$aiPercPart2 = execs$AIper2
execs$BQr1 = execs$BQr1
execs$BQr2 = execs$BQr2
execs$BQa1 = execs$BQa1
execs$BQa2 = execs$BQa2
execs$CQ1 = execs$CQ1
execs$CQ2 = execs$CQ2
execs$rho1 = (execs$Rho1)/1000
execs$rho2 = (execs$Rho2)/1000
execs$difPart1difPart2 = execs$DIF1divDIF2
execs$type = "Executive"
execs = cbind(execs[,48:58], execs[,38:39], execs[59:72], execs[,40:41], execs[,73:75], execs[,42:47], execs[,76:79])
execs[, 1:41] = sapply(execs[, 1:41], as.numeric)
execs$type = factor(execs$type)
# colStus import and cleaning
colStus = read_csv("CollegeStudents.csv")
colStus = colStus[,c(14:15,17:50,57:67)]
colStus$dimIPart1 = colStus$DIMI1
colStus$dimEPart1 = colStus$DIME1
colStus$dimSPart1 = colStus$DIMS1
colStus$intIPart1 = colStus$INTI1
colStus$intEPart1 = colStus$INTE1
colStus$intSPart1 = colStus$INTS1
colStus$difPart1 = colStus$DIF1
colStus$intPart1 = colStus$INT1
colStus$dimPart1 = colStus$DIM1
colStus$diPart1 = colStus$DI1
colStus$disPart1 = colStus$DIS1
colStus$VQ1 = colStus$VQ1
colStus$VQ2 = colStus$VQ2
colStus$dimPercPart1 = colStus$DIMper1
colStus$intPercPart1 = colStus$INTper1
colStus$aiPercPart1 = (colStus$AIper1)
colStus$dimIPart2 = colStus$DIMI2
colStus$dimEPart2 = colStus$DIME2
colStus$dimSPart2 = colStus$DIMS2
colStus$intIPart2 = colStus$INTI2
colStus$intEPart2 = colStus$INTE2
colStus$intSPart2 = colStus$INTS2
colStus$difPart2 = colStus$DIF2
colStus$intPart2 = colStus$INT2
colStus$dimPart2 = colStus$DIM2
colStus$diPart2 = colStus$DI2
colStus$disPart2 = colStus$DIS2
colStus$SQ1 = colStus$SQ1
colStus$SQ2 = colStus$SQ2
colStus$dimPercPart2 = colStus$DIMper2
colStus$intPercPart2 = colStus$INTper2
colStus$aiPercPart2 = (colStus$AIper2)
colStus$BQr1 = colStus$BQr1
colStus$BQr2 = colStus$BQR2
colStus$BQa1 = colStus$BQa1
colStus$BQa2 = colStus$BQa2
colStus$CQ1 = colStus$CQ1
colStus$CQ2 = colStus$CQ2
colStus$rho1 = colStus$Rho1
colStus$rho2 = colStus$Rho2
colStus$difPart1difPart2 = colStus$DIF1divDIF2
colStus$type = "CollegeStudent"
colStus = cbind(colStus[,48:58], colStus[,38:39], colStus[59:72], colStus[,40:41], colStus[,73:75], colStus[,42], colStus[,76], colStus[,44:47], colStus[,77:80])
colStus[, 1:41] = sapply(colStus[, 1:41], as.numeric)
colStus$type = factor(colStus$type)
colStus = na.omit(colStus)
colStus$aiPercPart1 = (colStus$aiPercPart1) /100
colStus$aiPercPart2 = (colStus$aiPercPart2) /100
colStus$dimPercPart1 = (colStus$dimPercPart1) /100
colStus$dimPercPart2 = (colStus$dimPercPart2) /100
colStus$intPercPart1 = (colStus$intPercPart1) /100
colStus$intPercPart2 = (colStus$intPercPart2) /100
colStus$difPart1difPart2 = (colStus$difPart1difPart2) / 100
# entreps import and cleaning
entreps = read_csv("Entrepreneurs.csv")
entreps = entreps[,c(15:51, 58:68)]
entreps$dimIPart1 = entreps$DIMI1
entreps$dimEPart1 = entreps$DIME1
entreps$dimSPart1 = entreps$DIMS1
entreps$intIPart1 = entreps$INTI1
entreps$intEPart1 = entreps$INTE1
entreps$intSPart1 = entreps$INTS1
entreps$difPart1 = entreps$DIF1
entreps$intPart1 = entreps$INT1
entreps$dimPart1 = entreps$DIM1
entreps$diPart1 = entreps$DI1
entreps$disPart1 = entreps$DIS1
entreps$VQ1 = entreps$VQ1
entreps$VQ2 = entreps$VQ2
entreps$dimPercPart1 = entreps$DIMper1
entreps$intPercPart1 = entreps$INTper1
entreps$aiPercPart1 = (entreps$AIper1)
entreps$dimIPart2 = entreps$DIMI2
entreps$dimEPart2 = entreps$DIME2
entreps$dimSPart2 = entreps$DIMS2
entreps$intIPart2 = entreps$INTI2
entreps$intEPart2 = entreps$INTE2
entreps$intSPart2 = entreps$INTS2
entreps$difPart2 = entreps$DIF2
entreps$intPart2 = entreps$INT2
entreps$dimPart2 = entreps$DIM2
entreps$diPart2 = entreps$DI2
entreps$disPart2 = entreps$DIS2
entreps$SQ1 = entreps$SQ1
entreps$SQ2 = entreps$SQ2
entreps$dimPercPart2 = entreps$DIMper2
entreps$intPercPart2 = entreps$INTper2
entreps$aiPercPart2 = (entreps$AIper2)
entreps$BQr1 = entreps$BQr1
entreps$BQr2 = entreps$BQR2
entreps$BQa1 = entreps$BQa1
entreps$BQa2 = entreps$BQa2
entreps$CQ1 = entreps$CQ1
entreps$CQ2 = entreps$CQ2
entreps$rho1 = entreps$Rho1
entreps$rho2 = entreps$Rho2
entreps$difPart1difPart2 = entreps$DIF1divDIF2
entreps$type = "Entrepreneur"
entreps = cbind(entreps[,49:59], entreps[,39:40], entreps[60:73], entreps[,41:42], entreps[,74:76], entreps[,43], entreps[,77], entreps[,45:48], entreps[,78:81])
entreps[, 1:41] = sapply(entreps[, 1:41], as.numeric)
entreps$type = factor(entreps$type)
entreps$aiPercPart1 = (entreps$aiPercPart1) /100
entreps$aiPercPart2 = (entreps$aiPercPart2) /100
entreps$dimPercPart1 = (entreps$dimPercPart1) /100
entreps$dimPercPart2 = (entreps$dimPercPart2) /100
entreps$intPercPart1 = (entreps$intPercPart1) /100
entreps$intPercPart2 = (entreps$intPercPart2) /100
entreps$difPart1difPart2 = (entreps$difPart1difPart2) / 100
# senMans importing and cleaning
senMans = read_csv("SeniorMgrs.csv")
senMans = senMans[,c(15:16, 18:51, 58:68)]
senMans$dimIPart1 = senMans$DIMI1
senMans$dimEPart1 = senMans$DIME1
senMans$dimSPart1 = senMans$DIMS1
senMans$intIPart1 = senMans$INTI1
senMans$intEPart1 = senMans$INTE1
senMans$intSPart1 = senMans$INTS1
senMans$difPart1 = senMans$DIF1
senMans$intPart1 = senMans$INT1
senMans$dimPart1 = senMans$DIM1
senMans$diPart1 = senMans$DI1
senMans$disPart1 = senMans$DIS1
senMans$VQ1 = senMans$VQ1
senMans$VQ2 = senMans$VQ2
senMans$dimPercPart1 = senMans$DIMper1
senMans$intPercPart1 = senMans$INTper1
senMans$aiPercPart1 = (senMans$AIper1)
senMans$dimIPart2 = senMans$DIMI2
senMans$dimEPart2 = senMans$DIME2
senMans$dimSPart2 = senMans$DIMS2
senMans$intIPart2 = senMans$INTI2
senMans$intEPart2 = senMans$INTE2
senMans$intSPart2 = senMans$INTS2
senMans$difPart2 = senMans$DIF2
senMans$intPart2 = senMans$INT2
senMans$dimPart2 = senMans$DIM2
senMans$diPart2 = senMans$DI2
senMans$disPart2 = senMans$DIS2
senMans$SQ1 = senMans$SQ1
senMans$SQ2 = senMans$SQ2
senMans$dimPercPart2 = senMans$DIMper2
senMans$intPercPart2 = senMans$INTper2
senMans$aiPercPart2 = (senMans$AIper2)
senMans$BQr1 = senMans$BQr1
senMans$BQr2 = senMans$BQr2
senMans$BQa1 = senMans$BQa1
senMans$BQa2 = senMans$BQa2
senMans$CQ1 = senMans$CQ1
senMans$CQ2 = senMans$CQ2
senMans$rho1 = senMans$Rho1
senMans$rho2 = senMans$Rho2
senMans$difPart1difPart2 = senMans$DIF1divDIF2
senMans$type = "SeniorManager"
senMans = cbind(senMans[,48:58], senMans[,38:39], senMans[59:72], senMans[,40:41], senMans[,73:75], senMans[,42:47], senMans[,76:79])
senMans[, 1:41] = sapply(senMans[, 1:41], as.numeric)
senMans$type = factor(senMans$type)
senMans = na.omit(senMans)
senMans$aiPercPart1 = (senMans$aiPercPart1) /100
senMans$aiPercPart2 = (senMans$aiPercPart2) /100
senMans$dimPercPart1 = (senMans$dimPercPart1) /100
senMans$dimPercPart2 = (senMans$dimPercPart2) /100
senMans$intPercPart1 = (senMans$intPercPart1) /100
senMans$intPercPart2 = (senMans$intPercPart2) /100
senMans$difPart1difPart2 = (senMans$difPart1difPart2) / 100
# Binding datasets together to analyze and draw out differences between groups
comb = rbind(execs, colStus, entreps, senMans)
comb[, 1:41] = sapply(comb[, 1:41], as.numeric)
comb$type = factor(comb$type)

EDA

a = ggplot() +
  geom_density(aes(x = execs$CQ1), alpha = 0.5, fill = "blue") +
  geom_density(aes(x = colStus$CQ1), alpha = 0.5, fill = "green") + 
  geom_density(aes(x = entreps$CQ1), alpha = 0.5, fill = "red") +
  geom_density(aes(x = senMans$CQ1), alpha = 0.5, fill = "black") +
  labs(x = "CQ1")
b = ggplot() +
  geom_density(aes(x = execs$rho1), alpha = 0.5, fill = "blue") +
  geom_density(aes(x = colStus$rho1), alpha = 0.5, fill = "green") + 
  geom_density(aes(x = entreps$rho1), alpha = 0.5, fill = "red") +
  geom_density(aes(x = senMans$rho1), alpha = 0.5, fill = "black") +
  labs(x = "Rho1")
c = ggplot() +
  geom_density(aes(x = execs$rho2), alpha = 0.5, fill = "blue") +
  geom_density(aes(x = colStus$rho2), alpha = 0.5, fill = "green") + 
  geom_density(aes(x = entreps$rho2), alpha = 0.5, fill = "red") +
  geom_density(aes(x = senMans$rho2), alpha = 0.5, fill = "black") +
  labs(x = "Rho2")
e = ggplot() +
  geom_density(aes(x = execs$aiPercPart1), alpha = 0.5, fill = "blue") +
  geom_density(aes(x = colStus$aiPercPart1), alpha = 0.5, fill = "green") + 
  geom_density(aes(x = entreps$aiPercPart1), alpha = 0.5, fill = "red") +
  geom_density(aes(x = senMans$aiPercPart1), alpha = 0.5, fill = "black") +
  labs(x = "AI Percentage Part 1")
f = ggplot() +
  geom_density(aes(x = execs$aiPercPart2), alpha = 0.5, fill = "blue") +
  geom_density(aes(x = colStus$aiPercPart2), alpha = 0.5, fill = "green") + 
  geom_density(aes(x = entreps$aiPercPart2), alpha = 0.5, fill = "red") +
  geom_density(aes(x = senMans$aiPercPart2), alpha = 0.5, fill = "black") +
  labs(x = "AI Percentage Part 2")
grid.arrange(a, b, c, e, f, ncol = 2)

Questions

1. Are rho1 and rho2 correlated in practice?
2. do rho1 scores between samples differ
3. Take samples of execs to examine between categories.
4. Is the correlation that’s baked into the model present in corelations

Testing

ggplot(comb, aes(rho1, rho2)) + geom_point(alpha = 0.5, aes(color = type))

cor(comb$rho1, comb$rho2)

[1] 0.2192963

pcaentreps = prcomp(entreps[1:41], scale = TRUE, center = TRUE)
pcaentreps$rotation[1:41,1:7]

                         PC1          PC2          PC3          PC4          PC5           PC6          PC7
dimIPart1        -0.12069640 -0.123524888 -0.280651425  0.103192230 -0.140186166  0.3601000406 -0.058300903
dimEPart1        -0.06244202 -0.131777436 -0.267692196 -0.103567015  0.249638635 -0.4236877477  0.016973018
dimSPart1        -0.12129789 -0.176498626  0.213245707 -0.042604505 -0.088937855  0.0450857224  0.116988731
intIPart1        -0.13523631 -0.123565782 -0.280311962  0.079127382 -0.085743348  0.3062872682 -0.055220989
intEPart1        -0.08515984 -0.134503686 -0.261684043 -0.071197550  0.217393685 -0.4092140176  0.041656885
intSPart1        -0.13530821 -0.165022540  0.195992944 -0.015313083 -0.102744990  0.0781306460  0.214645690
difPart1         -0.15628544 -0.215867376 -0.172407332 -0.008182514 -0.013391155  0.0398166053  0.032250141
intPart1         -0.17438950 -0.202501096 -0.157256269  0.002532267 -0.010297598  0.0319369463  0.090578039
dimPart1         -0.06277267 -0.183905574  0.377175381 -0.022544389 -0.057504248 -0.0382445349 -0.140096222
diPart1          -0.10775254 -0.189272693  0.272535905  0.023795344 -0.091789486  0.0332984473 -0.084088565
disPart1         -0.08321179 -0.168482833  0.057078014 -0.168862544  0.247375071 -0.1503491941 -0.177533817
VQ1              -0.15831495 -0.245597763  0.011909938 -0.024490278 -0.010832894  0.0027331458 -0.020443285
VQ2              -0.14314593 -0.241631634  0.146325147 -0.033916151 -0.007809680 -0.0248502082 -0.057077175
dimPercPart1      0.00808881 -0.110186938  0.434803390 -0.040170113 -0.074955568 -0.0941064939 -0.156408176
intPercPart1     -0.16125711 -0.184561676 -0.120559394  0.025736112 -0.042327465  0.0356566629  0.178990259
aiPercPart1      -0.08767945 -0.174959392  0.055158165 -0.100104020  0.305772891 -0.1422498725 -0.275044916
dimIPart2        -0.14776329  0.108864476 -0.029845360  0.057100406 -0.378755788 -0.3338790647  0.110127024
dimEPart2        -0.14984317  0.078383533  0.098475449 -0.226210961  0.245206584  0.1547649967  0.407762743
dimSPart2        -0.15784804  0.113894963 -0.084276880 -0.205835540 -0.024346189  0.1483906850 -0.414381995
intIPart2        -0.14574559  0.107317952 -0.040087884  0.105386826 -0.366006609 -0.3714411657  0.044759095
intEPart2        -0.14870418  0.081157562  0.114404191 -0.199116157  0.272347220  0.1618139879  0.392669767
intSPart2        -0.15699080  0.109900319 -0.070125675 -0.215041727 -0.021961821  0.1514463262 -0.419012123
difPart2         -0.20579000  0.142507817 -0.020173813 -0.171594370 -0.050757919  0.0104991124  0.051997341
intPart2         -0.21602834  0.142777668  0.000491846 -0.154860432 -0.048818105 -0.0160505316 -0.005328665
dimPart2         -0.15728419  0.054306716  0.073514826  0.402026971  0.198725715  0.0116993945 -0.005629773
diPart2          -0.18607730  0.070913399  0.044816612  0.327639052  0.059674961 -0.0160941564  0.011586406
disPart2         -0.18109900  0.027291162 -0.029184098  0.061448936 -0.174305545 -0.0083761239 -0.057231054
SQ1              -0.23058673  0.131511815  0.017326106 -0.013030958  0.006481007 -0.0005600189  0.010428703
SQ2              -0.22807667  0.115410176  0.035055041  0.121762523  0.054970741 -0.0043685680 -0.012105962
dimPercPart2     -0.05987428 -0.005804932  0.080996475  0.504171274  0.276227716  0.0216252630 -0.018593912
intPercPart2     -0.19381799  0.149751132  0.007383423 -0.157290033 -0.011865121 -0.0523715281  0.038751384
aiPercPart2      -0.18533531  0.031240128  0.027323392  0.102086324 -0.150696697 -0.0446281282  0.060737081
BQr1             -0.06139525  0.294337515  0.012297982  0.023297723  0.092567027 -0.0217626548 -0.016483125
BQr2             -0.03688526  0.256881502 -0.043190282  0.122198449  0.144006618  0.0028720991 -0.081220726
BQa1             -0.25182578 -0.047709376  0.017181977 -0.022982853 -0.003383479  0.0034339226 -0.004768524
BQa2             -0.24208711 -0.063070666  0.108615610  0.067582221  0.032022592 -0.0159416656 -0.044311485
CQ1              -0.17398706  0.127401411  0.045979177 -0.001851696  0.177035457  0.0696551636 -0.089196501
CQ2              -0.16992315  0.153285395  0.027979947  0.194281466  0.103424143 -0.0473821128 -0.125393284
rho1              0.16854235  0.199082824  0.171609566 -0.013317910  0.022145953 -0.0518230246 -0.027825327
rho2              0.22307773 -0.132955784  0.004136560  0.103965707  0.064312283  0.0320682178 -0.005176128
difPart1difPart2  0.05300314 -0.271927572 -0.121915454  0.167068508  0.015581164  0.0221992232 -0.036148907

biplot(pcaentreps)

entsenman = rbind(entreps, senMans)
pcaentsenman = prcomp(entsenman[1:41], scale = TRUE, center = TRUE)
summary(pcaentsenman)

Importance of components:
                          PC1    PC2     PC3     PC4     PC5    PC6     PC7     PC8     PC9    PC10    PC11    PC12    PC13
Standard deviation     3.7484 3.2900 1.84657 1.65201 1.30616 1.2132 1.17301 1.09879 0.98394 0.94910 0.72210 0.53346 0.50178
Proportion of Variance 0.3427 0.2640 0.08317 0.06656 0.04161 0.0359 0.03356 0.02945 0.02361 0.02197 0.01272 0.00694 0.00614
Cumulative Proportion  0.3427 0.6067 0.68987 0.75644 0.79805 0.8339 0.86750 0.89695 0.92057 0.94254 0.95525 0.96219 0.96834
                          PC14   PC15    PC16    PC17   PC18    PC19    PC20    PC21    PC22    PC23    PC24    PC25    PC26
Standard deviation     0.48097 0.4344 0.40233 0.35836 0.3201 0.30274 0.25351 0.24730 0.22923 0.20710 0.19887 0.18267 0.16760
Proportion of Variance 0.00564 0.0046 0.00395 0.00313 0.0025 0.00224 0.00157 0.00149 0.00128 0.00105 0.00096 0.00081 0.00069
Cumulative Proportion  0.97398 0.9786 0.98253 0.98566 0.9882 0.99040 0.99196 0.99346 0.99474 0.99578 0.99675 0.99756 0.99825
                          PC27    PC28    PC29    PC30    PC31    PC32    PC33    PC34    PC35     PC36      PC37      PC38
Standard deviation     0.14635 0.12490 0.10711 0.09949 0.08871 0.06077 0.03549 0.01775 0.01602 0.009332 7.284e-16 4.765e-16
Proportion of Variance 0.00052 0.00038 0.00028 0.00024 0.00019 0.00009 0.00003 0.00001 0.00001 0.000000 0.000e+00 0.000e+00
Cumulative Proportion  0.99877 0.99915 0.99943 0.99967 0.99986 0.99995 0.99998 0.99999 1.00000 1.000000 1.000e+00 1.000e+00
                            PC39     PC40     PC41
Standard deviation     4.558e-16 4.22e-16 3.57e-16
Proportion of Variance 0.000e+00 0.00e+00 0.00e+00
Cumulative Proportion  1.000e+00 1.00e+00 1.00e+00

ggplot(as.data.frame(pcaentsenman$x), aes(PC2, PC4)) + 
  geom_point(aes(color = entsenman$type))

Entreps vs SenMans

entsenman = rbind(entreps, senMans)
meltentsenman = melt(entsenman)

Using type as id variables

ggplot(meltentsenman) +
  geom_density(aes(x = value, fill = type), alpha = 0.5) +
  facet_wrap( ~ variable, scales = "free", ncol = 4)

confusionMatrix(preds, test$type)

Confusion Matrix and Statistics

               Reference
Prediction      Entrepreneur SeniorManager
  Entrepreneur            27            11
  SeniorManager           19            40
                                          
               Accuracy : 0.6907          
                 95% CI : (0.5888, 0.7807)
    No Information Rate : 0.5258          
    P-Value [Acc > NIR] : 0.0007024       
                                          
                  Kappa : 0.3745          
 Mcnemar's Test P-Value : 0.2012426       
                                          
            Sensitivity : 0.5870          
            Specificity : 0.7843          
         Pos Pred Value : 0.7105          
         Neg Pred Value : 0.6780          
             Prevalence : 0.4742          
         Detection Rate : 0.2784          
   Detection Prevalence : 0.3918          
      Balanced Accuracy : 0.6856          
                                          
       'Positive' Class : Entrepreneur    
                                          

feature selection

ffs = regsubsets(type ~ ., data = entsenman, nvmax = 10)

5  linear dependencies found

Reordering variables and trying again:

summary(ffs)

Subset selection object
Call: regsubsets.formula(type ~ ., data = entsenman, nvmax = 10)
41 Variables  (and intercept)
                 Forced in Forced out
dimIPart1            FALSE      FALSE
dimEPart1            FALSE      FALSE
dimSPart1            FALSE      FALSE
intIPart1            FALSE      FALSE
intEPart1            FALSE      FALSE
intSPart1            FALSE      FALSE
intPart1             FALSE      FALSE
dimPart1             FALSE      FALSE
diPart1              FALSE      FALSE
disPart1             FALSE      FALSE
VQ1                  FALSE      FALSE
dimPercPart1         FALSE      FALSE
intPercPart1         FALSE      FALSE
aiPercPart1          FALSE      FALSE
dimIPart2            FALSE      FALSE
dimEPart2            FALSE      FALSE
dimSPart2            FALSE      FALSE
intIPart2            FALSE      FALSE
intEPart2            FALSE      FALSE
intSPart2            FALSE      FALSE
difPart2             FALSE      FALSE
dimPart2             FALSE      FALSE
diPart2              FALSE      FALSE
disPart2             FALSE      FALSE
dimPercPart2         FALSE      FALSE
intPercPart2         FALSE      FALSE
aiPercPart2          FALSE      FALSE
BQr1                 FALSE      FALSE
BQr2                 FALSE      FALSE
BQa1                 FALSE      FALSE
BQa2                 FALSE      FALSE
CQ1                  FALSE      FALSE
CQ2                  FALSE      FALSE
rho1                 FALSE      FALSE
rho2                 FALSE      FALSE
difPart1difPart2     FALSE      FALSE
difPart1             FALSE      FALSE
VQ2                  FALSE      FALSE
intPart2             FALSE      FALSE
SQ1                  FALSE      FALSE
SQ2                  FALSE      FALSE
1 subsets of each size up to 11
Selection Algorithm: exhaustive
          dimIPart1 dimEPart1 dimSPart1 intIPart1 intEPart1 intSPart1 difPart1 intPart1
1  ( 1 )  " "       " "       " "       " "       " "       " "       " "      " "     
2  ( 1 )  " "       " "       " "       " "       "*"       " "       " "      " "     
3  ( 1 )  " "       " "       " "       " "       " "       " "       "*"      " "     
4  ( 1 )  " "       " "       " "       " "       " "       " "       "*"      " "     
5  ( 1 )  " "       " "       " "       " "       " "       " "       "*"      " "     
6  ( 1 )  " "       " "       " "       " "       " "       " "       "*"      " "     
7  ( 1 )  " "       " "       " "       " "       " "       " "       "*"      " "     
8  ( 1 )  " "       " "       " "       " "       " "       " "       "*"      " "     
9  ( 1 )  " "       " "       " "       " "       " "       " "       "*"      " "     
10  ( 1 ) " "       " "       " "       " "       " "       " "       "*"      " "     
11  ( 1 ) " "       " "       " "       " "       " "       " "       "*"      " "     
          dimPart1 diPart1 disPart1 VQ1 VQ2 dimPercPart1 intPercPart1 aiPercPart1 dimIPart2
1  ( 1 )  " "      " "     " "      " " " " " "          " "          " "         " "      
2  ( 1 )  " "      " "     " "      " " " " " "          " "          " "         " "      
3  ( 1 )  " "      " "     " "      "*" "*" " "          " "          " "         " "      
4  ( 1 )  " "      " "     "*"      "*" "*" " "          " "          " "         " "      
5  ( 1 )  " "      " "     "*"      " " "*" " "          " "          " "         " "      
6  ( 1 )  " "      " "     "*"      "*" "*" " "          " "          " "         " "      
7  ( 1 )  " "      " "     "*"      "*" "*" " "          " "          " "         "*"      
8  ( 1 )  " "      " "     "*"      "*" "*" " "          " "          " "         "*"      
9  ( 1 )  " "      " "     "*"      "*" "*" " "          " "          " "         "*"      
10  ( 1 ) " "      " "     "*"      "*" "*" " "          " "          " "         "*"      
11  ( 1 ) " "      " "     "*"      "*" "*" " "          " "          " "         "*"      
          dimEPart2 dimSPart2 intIPart2 intEPart2 intSPart2 difPart2 intPart2 dimPart2
1  ( 1 )  " "       " "       " "       " "       " "       " "      " "      " "     
2  ( 1 )  " "       " "       " "       " "       " "       " "      " "      " "     
3  ( 1 )  " "       " "       " "       " "       " "       " "      " "      " "     
4  ( 1 )  " "       " "       " "       " "       " "       " "      " "      " "     
5  ( 1 )  " "       " "       " "       " "       " "       " "      " "      " "     
6  ( 1 )  " "       " "       " "       " "       " "       " "      " "      " "     
7  ( 1 )  " "       " "       " "       " "       " "       " "      " "      " "     
8  ( 1 )  " "       " "       " "       "*"       " "       " "      " "      " "     
9  ( 1 )  " "       " "       " "       "*"       " "       " "      " "      " "     
10  ( 1 ) " "       "*"       " "       "*"       " "       " "      " "      " "     
11  ( 1 ) " "       "*"       " "       "*"       " "       " "      " "      " "     
          diPart2 disPart2 SQ1 SQ2 dimPercPart2 intPercPart2 aiPercPart2 BQr1 BQr2 BQa1
1  ( 1 )  " "     " "      " " " " " "          " "          " "         " "  " "  " " 
2  ( 1 )  " "     " "      " " " " " "          " "          " "         " "  " "  " " 
3  ( 1 )  " "     " "      " " " " " "          " "          " "         " "  " "  " " 
4  ( 1 )  " "     " "      " " " " " "          " "          " "         " "  " "  " " 
5  ( 1 )  " "     " "      "*" " " " "          " "          " "         " "  " "  "*" 
6  ( 1 )  " "     " "      " " "*" " "          " "          " "         " "  " "  " " 
7  ( 1 )  " "     " "      " " "*" " "          " "          " "         " "  " "  " " 
8  ( 1 )  " "     " "      " " "*" " "          " "          " "         " "  " "  " " 
9  ( 1 )  " "     " "      " " "*" " "          " "          " "         " "  " "  " " 
10  ( 1 ) " "     " "      " " "*" " "          " "          " "         " "  " "  " " 
11  ( 1 ) " "     " "      " " "*" " "          " "          " "         " "  " "  " " 
          BQa2 CQ1 CQ2 rho1 rho2 difPart1difPart2
1  ( 1 )  " "  "*" " " " "  " "  " "             
2  ( 1 )  " "  "*" " " " "  " "  " "             
3  ( 1 )  " "  " " " " " "  " "  " "             
4  ( 1 )  " "  " " " " " "  " "  " "             
5  ( 1 )  " "  " " " " " "  " "  " "             
6  ( 1 )  "*"  " " " " " "  " "  " "             
7  ( 1 )  "*"  " " " " " "  " "  " "             
8  ( 1 )  "*"  " " " " " "  " "  " "             
9  ( 1 )  "*"  " " " " " "  "*"  " "             
10  ( 1 ) "*"  " " " " " "  "*"  " "             
11  ( 1 ) "*"  " " " " " "  "*"  "*"             

a = data.frame(x = rep(1:42), y = ffs$rss)
ggplot(a, aes(x, y)) + geom_point() + labs(x = "# of Features", y = "RSS")

Important variables from FFS are:

ffs$xnames[c(6, 9, 19, 22, 27, 39)]

[1] "intEPart1"    "dimPart1"     "intIPart2"    "difPart2"     "intPercPart2" "VQ2"         

Variables where the 2 groups differ:

# differ
print("Variables that differ between groups:")

[1] "Variables that differ between groups:"

for (i in names(entsenman)[1:41]) {
  a = wilcox.test(get(i) ~ type, data = entsenman)
  if (a$p.value < 0.05) {
    print(c(i, a$p.value))
  }
}

[1] "dimEPart1"           "0.00240878216306191"
[1] "dimSPart1"           "0.00998679439625931"
[1] "intEPart1"            "0.000414251429586648"
[1] "intSPart1"          "0.0128787501043578"
[1] "difPart1"           "0.0311585017446253"
[1] "intPart1"           "0.0209344920686297"
[1] "VQ1"                "0.0287057955786282"
[1] "VQ2"                "0.0140518727038859"
[1] "intPercPart1"       "0.0204723685155504"
[1] "dimIPart2"           "0.00118297965230699"
[1] "intIPart2"           "0.00470298154277639"
[1] "difPart2"           "0.0287260180393314"
[1] "BQr1"                "0.00326264371202953"
[1] "BQr2"                "0.00392589669009157"
[1] "CQ1"                  "1.31308755229483e-06"
[1] "CQ2"                  "2.95684186641073e-07"
[1] "rho1"                "0.00735204490117357"
[1] "difPart1difPart2"    "0.00106469953419607"

print(" ")

[1] " "

# don't differ
print("Variables that don't differ between groups:")

[1] "Variables that don't differ between groups:"

for (i in names(entsenman)[1:41]) {
  a = wilcox.test(get(i) ~ type, data = entsenman)
  if (a$p.value > 0.05) {
    print(c(i, a$p.value))
  }
}

[1] "dimIPart1"         "0.484564468983294"
[1] "intIPart1"         "0.352122291646371"
[1] "dimPart1"          "0.168509457529553"
[1] "diPart1"           "0.274930934966402"
[1] "disPart1"          "0.911874291987055"
[1] "dimPercPart1"      "0.726297483135801"
[1] "aiPercPart1"       "0.888167633589448"
[1] "dimEPart2"          "0.0556588112955014"
[1] "dimSPart2"         "0.868425305958607"
[1] "intEPart2"        "0.25890114674539"
[1] "intSPart2"         "0.831856245784447"
[1] "intPart2"          "0.101932976083815"
[1] "dimPart2"          "0.648539642288582"
[1] "diPart2"           "0.295206337448447"
[1] "disPart2"           "0.0761111547877471"
[1] "SQ1"                "0.0539467038098364"
[1] "SQ2"               "0.164549556351549"
[1] "dimPercPart2"      "0.547675988143944"
[1] "intPercPart2"     "0.49441217619342"
[1] "aiPercPart2"       "0.100255607484888"
[1] "BQa1"              "0.869720709150679"
[1] "BQa2"              "0.740919679141109"
[1] "rho2"              "0.121063525116053"

EFA in R

covMat = cov(comb[1:41])
### some covariance is too high, need to remove variables that covary too much to run factor analysis!
factors = factanal(covmat = covMat, factors = 7, n.obs = nrow(comb), rotation = "varimax")

Error in solve.default(cv) : 
  system is computationally singular: reciprocal condition number = 3.20404e-19